What is the maximum intensity in case of interference of $n$ identical waves each of intensity $I_0$, if the interference is (a) coherent (b) incoherent.

(a) The resulting intensity is given by 

$$\begin{gathered} \mathrm{I}={\mathrm{I}}_1+{\mathrm{I}}_2+2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2} \cos \mathrm{\varphi } \\ \mathrm{and} {\mathrm{I}}_{\max }={\left(\sqrt{{\mathrm{I}}_1}+\sqrt{{\mathrm{I}}_2}\right)}^2 \end{gathered}$$

For $n$ identical waves of each intensity $I_0$,

${\mathrm{I}}_{\max }={\left(\sqrt{{\mathrm{I}}_0}+\sqrt{{\mathrm{I}}_0}+.....\mathrm{n} \mathrm{times}\right)}^2={\mathrm{n}}^2{\mathrm{I}}_0$

(b) When interference is incoherent then

$I_{max}=I_1+I_2$

For $n$ identical waves each of intensity $I_0$ then

${\mathrm{I}}_{\max }={\mathrm{I}}_0+{\mathrm{I}}_0+.....\mathrm{n} \mathrm{times}={\mathrm{nI}}_0$